As　one　of　the　most　important　indexes　to　evaluate　the　quality　of　software,　software　reliability　experiences　an　increasing　development　in　recent　years.　We　investigate　a　software　reliability　growth　model　(SRGM).　The　application　of　this　model　is　to　predict　the　occurrence　of　the　software　faults　based　on　the　non-homogeneous　Poisson　process　(NHPP).　Unlike　the　independent　assumptions　in　other　models,　we　consider　fault　dependency.　The　testing　faults　are　divided　into　three　classes　in　this　model:　leading　faults,　first-step　dependent　faults　and　second-step　dependent　faults.　The　leading　faults　occurring　independently　follow　an　NHPP,　while　the　first-step　dependent　faults　only　become　detectable　after　the　related　leading　faults　are　detected.　The　second-step　dependent　faults　can　only　be　detected　after　the　related　first-step　dependent　faults　are　detected.　Then,　the　combined　model　is　built　on　the　basis　of　the　three　sub-processes.　Finally,　an　illustration　based　on　real　dataset　is　presented　to　verify　the　proposed　model.　©　2019,　Shanghai　Jiao　Tong　University　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.